Best Known (109, 109+36, s)-Nets in Base 3
(109, 109+36, 328)-Net over F3 — Constructive and digital
Digital (109, 145, 328)-net over F3, using
- 31 times duplication [i] based on digital (108, 144, 328)-net over F3, using
- trace code for nets [i] based on digital (0, 36, 82)-net over F81, using
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 0 and N(F) ≥ 82, using
- the rational function field F81(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 81)-sequence over F81, using
- trace code for nets [i] based on digital (0, 36, 82)-net over F81, using
(109, 109+36, 680)-Net over F3 — Digital
Digital (109, 145, 680)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3145, 680, F3, 36) (dual of [680, 535, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3145, 728, F3, 36) (dual of [728, 583, 37]-code), using
(109, 109+36, 26320)-Net in Base 3 — Upper bound on s
There is no (109, 145, 26321)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 1523 477832 909500 059293 529818 560412 303103 625519 004060 748809 260533 088617 > 3145 [i]